Reni
Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?
(1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate
(2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate
Statement 1 :-
Say , Machine M produces x nails / hour and machine N produces (x +2000 ) nails / hour.
Machine M worked for = 6000/x hours.
Machine N worked for = 8000 / (x + 2000) hours.
The denominator is not same . We cant tell whether 6000/x > 8000/(x+2000)
It depends on the value of x.
Statement 2:-
Say , Machine M produces x nails / hour and machine N produces 2*x nails / hour.
So, Machine M worked for = 6000/x hours.
Machine N worked for = 8000 /2*x hours = 4000/x hours
Since the denominator is fixed , we can say YES , machine M work longer than machine N.
Take a fixed denominator for example , x = 2
6000 / 2 = 3000
4000/2 = 2000
3000 > 2000
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